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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 263, page id 1066518432:0291
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DE VIRTDOSEF MOTIBOS CORDORUM. L. 1B. II. 263
459. PONAMUS VeTO NOMINatAS CUEVAS AC F eE A2BF. similes et
aequales esse, quo ACE UE aECUS FB ex A2B aequales sinE; cum linexe
BB ec 2B2B, ipE AT (secundum hypochesin) Parallelae, arcus in B
_ 2B COnLInSANE, PrOPterCa CrunE H HI = A2II, item BII = 2B2TI,
atque adeo IID =D2HI, nec non producta 2B2II usque ad OcCur-
sum ejuS CuErX F. C A in ZB, Aet 2tI3B =2B2HI = BII, aC per CON-
seguens linea BF, ip( F A Parallela, SecaBIE CUEram RCR in puncto
3B, adco ut arcus BC _ CZB similes et aequales futuri sint. ITisce
politis reperietur AL = A2 + A3; BI =B2 FB3; C.F =C2 +C3 et
DT = D2 + D3; ac proinde hoc calu habebimus
AF = A2 + A3 = 2. A3 (Cu duPI2 (3.
BF + B2 =B3 = 2, B2.
CY + C2 - C3 =2. C2.
DF = D2 + D3 =2. D3. Adeoque hi ralores, in analogia praeceden:
tis parasraphi Tubrosati, prxbebunt AW: WVS = e. PZH F 4be. A3:
B; + (26be = 2aaC). B2: a, ad e. TI2FI; + 4be. C2: a; + (2bbe = 2aaC).
D3: aa, vel diridendo terminos per 20, Sicut FA; + 2bA3: a; +
(bb = aa). B2: aa; 2d DFL; + 2bC2: a3 + (bb = aa). D3: aa; BENI:
AW = a: b; CrGO CX aequo crit WI: WVS =a. V A + 2b. A3; +
(bb = aa). B2: a, 2d b. DF; + 26b. C2: a; + (b3 = aab). DZ: aa; vel
rocando tangentem anguli dati SAWV, t; e tangentem quaeliti
TAW, O; habebimus D: Y = a. F A + 2aab. A3; + (ab b = a). B2: aab.
DII, + 2abb. C2, + (B = aab) D3; adeoque, multiplicando extrema
de media, habebimus aequationem lequentem generalem a’t. F A +
2aabt. A3 + (abbt - a. t). B2 = aabb. DIL, + 24b6d. C2, + (bd = aabd).
D3. In qua aequatione loco magnitudinum FA, DH, A3; B2,
C2 eE D3 Subrocandi Tunt carum valores, quos praebebitnatura Cur-
ra AZBC expressi quanticatibus a, b, aliisque constantibus; posi.
tisque loco b, radtii sou sinus torius nomine r, et loco ipsius a nO-
mine tansentis quaelitae o, habebitur aequatio in Cola D et quantita-
tibus constantibus leu cognitis data, cujus aequationis radices. ma-
nifeltabunt ralorem tangentis anguli quaeliti PAW.
460. F X E M DL. SInE CUEVR ACF _ A2BF arcus aequales ali-
cujus circuli, cujus radius =e, aC SinUS Complementi arCUS AC, qui
eA LemissIS FOEIUS ACF vel A2BE, dicatuE B, SInEque B3: 3ee =R,.
et h = B = l, InVeNIENFARqUC A3 = a’ C: 3C3, B2 = l; + be: C; = b e: 3C3,
C2 = b e: 35; =R, ac denique DZ = a e: 3C. PRUNE POrrO AF vel
BH = be: C; = B, _ DEI vel D2HI =ae: C; qui ralores in xequatio.
ne generali substicuri, Fractionum reductionibus ad nomen z0 rite.
Der-